Staff: Mentor

Could someone help me solve this? I can't seem to find a substitution that works, or find the square root of (x^4/4 + 1/(x^4). Any help would be very appreciated.

Thanks in advance!

What's inside the radical is almost a perfect square, so it's possible that you have made an error in the work leading up to the integral. Please show the function whose arc length you're trying to find, and what you did to get your integral.

What's inside the radical is almost a perfect square, so it's possible that you have made an error in the work leading up to the integral. Please show the function whose arc length you're trying to find, and what you did to get your integral.

Also, I hope this isn't how you're doing your work. Instead of starting each line with L = ... and dragging the integral along at each step, it's much easier, and easier to read, if you write down what you need for the step at hand. In other words, find the derivative, square it, add 1, and take the square root. That will be your integrand. Each step from then on until you evaluate the integral will show the integral symbol, but you don't need it in the steps leading up to getting the integrand.

I see that you didn't use the homework template, which has a section for the problem statement. Without knowing what the original problem was, I was not able to tell where you went wrong. This is one reason why we ask that you include this information. Please include the problem statement in any future posts.

Your mistake is in the next line. Notice that you have a sign error and an error in the coefficient.
If y = (1/6)x3 + 1/(2x), y' = (1/2)x2 - 1/(2x2)

Also, I hope this isn't how you're doing your work. Instead of starting each line with L = ... and dragging the integral along at each step, it's much easier, and easier to read, if you write down what you need for the step at hand. In other words, find the derivative, square it, add 1, and take the square root. That will be your integrand. Each step from then on until you evaluate the integral will show the integral symbol, but you don't need it in the steps leading up to getting the integrand.

I see that you didn't use the homework template, which has a section for the problem statement. Without knowing what the original problem was, I was not able to tell where you went wrong. This is one reason why we ask that you include this information. Please include the problem statement in any future posts.

Thank you for being so patient with me. I'm 15 and have very little clue what I'm doing. I skipped Algebra II and Precalculus (testing out of them by the skin of my teeth.)

That was probably not a good idea. In any case, for the areas in which you're weak, it would be very helpful for you to review. You could pick up a precalculus textbook from Amazon or look at the algebra and precalc topic on khanacademy.org. Some time spent on a regular basis would be a very good investment.